Besides the ability to perceptually discriminate between units up to 7 or 8, @ExistenceUniversity asserted in his recent video that humans can also distinguish large ratios without counting. If you have 20 spears or 80 spears, you can clearly see that 20 is less than 80. As you said in your video, you would not be able to perceive 75 vs 80 vs 85 in the large pile, but we are doing something that makes comparing the groups immediately clear. I know some of our senses work on non-linear bases. Perhaps our visual system has two modes which we can use as the foundational fact to build our mathematical concepts.
@Inductica the most obvious problem is trying to infer your working definition of "mathematics" that fits the concept of "invented", but more specifically stated is the idea that there could have been a human society "where no one even knows how to count yet" which is contrary to established biology. In sum, the published work of: "Mathematical Cognition and Learning", by Michael J. Beran, Audrey E. Parrish, Theodore A. Evans, Volume 1, 2015, Pages 91-119, ISSN 2214-2568 says that according to research, primates are able to make ordinality judgments based on symbolic representations of numbers. This is a step above an beyond counting. It indicates that even the ancestors of the first humans could count innately. Counting for primates is similar to walking or eating. Its just something they can do.
As is borne out in the history of western mathematics, I would predict that some of man's earliest mathematics would come from music. But not because of harmony--because you very quickly need some kind of measurement system for precisely synchronizing events in time. Indeed, I posit that counting rhythms and cultural understandings of song and dance are probably man's earliest mathematics, even before we started forming sophisticated armies and trading with one another in sophisticated ways.
this depends largely on your definitions of both math and music. if counting is considered math - then primates naturally develop the skill much like walking or chewing. so you might need a working definition of music that can be applied to all adolescent primates.
Interesting video. Trying to put myself in the shoes of an ancient , fictional person like that helps me to think about all the ideas I hold and essentially take for granted.
8:09 ha! MArduk's soldeiers are wearing clothing with more than 7 tassels! Also they bands on their shoulders. We knew how to group and to count long before the neolithic. And the Egyptians were using scales LONG before the time of your "Marduk" in Babel.
Delighted to see you identify a method simpler than counting. This series is awesome. The rock carving adds to the story, but I think it has misled some of the commentators. This tribe from Babel is very ancient. They are not the people who had time to make such beautiful carvings or any monumental structures. What your story helps illustrate is the hierarchy of mathematical methods and to tease out methods we use all the time. We automated these comparison as well as the times tables. We don't normally notice them as a skill we learned or invented.
The quantities being compared are item quantities, not weights. And the uniformity of mass per item in this scenario has not been stipulated. So a comparison of weights here would not add value.
@@BuckPowers That's right, you are noticing how that his suggestion would break inductive order. I didn't even realize what his suggestion was at first.
Mathematics was invented before language. Language IS math. Counting was the beginning. Saying they invented language before counting is like saying they invented algebra before numbers.
@@ExistenceUniversity This quote is a non-sequitir: though concept formation has a mathematical nature, that does not mean man needs explicit mathematical concepts before forming concepts. Rand also said somewhere else that the field of mathematics makes explicit what is implicit in the process of concept formation. So the mathematics inherent in forming concepts is implicit only, it is not the same as what I'm developing here, and what Walter was talking about, which is explicit mathematical concepts and methods.
@@ExistenceUniversity Exactly. Although in the case of Socrates = Man it would be a little more nuanced than that, as all men are not Socrates, so you'd likely use a uni-directional associative symbol rather than bidirectional association, but the general premise you're talking about is correct. There's a recent interesting lecture you can find on RUclips called "Natural language as a cognitive computation on data-compressed grounded symbols" that covers this quite well and demonstrates the algebraic nature of language that is generally left out of the sentences we create for brevity, but still implied.
this is all over the place. Many animals have an innate ability to count - so it would be weird to say that counting was invented - was walking invented? Was burping invented? Is counting not "math"? math is not interesting until you can communicate mathematically which may or may not require other skills that we could recognize as language first, but it seems like communication/language is required first before any recognizable as math. The reason for this is simple - for math to function as math - it requires an agreement against contradiction. First before we can do math, we have to agree that contradiction is forbidden. Only then can we "have math" other than innate counting. So we need some natural language way to agree to exclude contradiction before we have anything like an effective math. It means natural language is a precursor to any significant math. Importantly, for humans, as the present condition we find ourselves in - there is no better way to understand math other than that it is a language exactly in the same way English is a language and Spanish is a language. The difference is that math has a rule to exclude contradiction and that rule incites agreement on definitions before trying to express mathematical ideas. After that - its just another language.
@@oversquare6625 Animals don't count. There's a difference between counting and knowing whether one group is larger than another group intuitively. Counting is a very specific process, and it requires assigning labels and iterating on labels.
The whole story seems to about the pragmatic significance of mathematics for survival which is mostly fine. Although as a platonist, i think it is a discovery not an invention. Also counting presupposes basic arithmetic capacity and i dont see a way around that being innate.
@@ReflectiveJourney In our next video, you will see how counting can be invented through observations and reasoning with knowledge established in this video. Respectfully, I’ll give my opinion about the metaphysical nature of math, which is in strong opposition to Platonism: I think quantities and quantitative facts are out there in the world (such as the quantity of troops Marduk has) and that we *invent* mathematical *methods* to grasp those quantities. So the quantities are metaphysical, number, counting and other mathematical methods are inventions for grasping these facts and making inferences about their relationships between one another.
@@Inductica I would need to know more about what is meant by "quantities" and how is it different from numbers. Do you just mean that there are quantifiable facts like "there are 2 apples on the table" where "2" is the counting method used to state the fact. Interesting view and i would agree with you that the methods and language to talk about mathematical structure is contingent on experience. This doesn't address the ontological issue though. In my view, there are no perfect identities in the material world and it is a feature of our cognitive capacities that we track "close enough" patterns in the experience. Mathematics is the study of pure structures. I don't take a dualist view, the physical world is rationally constrained by the forms. The Pythagorean theorem is constraining the 3rd side of a triangle if you pick any two sides. It is not a generalization but a discovery about a geometrical structure (triangle). Even if we don't have a pure triangle in material world still any close enough structure to the triangle would be constrained by that. i am just probably rephrasing what Plato meant that experiential world is just an image of the forms but i believe he was pretty close.
@@ReflectiveJourney Thank you for explaining your position clearly and respectfully. You have improved the quality of my comments section XD. Yes, that's very similar to Plato's view. In contrast, I think existence (the material world, as you put it) has full identity and that our senses give us data about that identity. If you'd like to know what my reason is for thinking that, check out the book "Objectivism, the Philosophy of Ayn Rand."
Why make a fiction? We have the ancient cuneiform tablets. We know that the origin story of writing is also the origin story of accounting. They invented credit money. The ancient near eastern maths were quite advanced. So, why the fiction?
Good question. Even if we adhered very closely to the ancient records, we would still have to fill in a lot of gaps regarding the actual observations and reasoning steps. Further, the actual history of math and physics involves lots of wrong turns and faulty reasoning. Our goal in this series is not to present a history of math, but rather to show its observational proof.
@@ExistenceUniversity You can see that these are situations which could happen, and that these are reasoning steps one could perform without knowing any math yet, the fictional nature of the narrative does not make it less rigorous.
While we know the sumerian tablets contain origin stories of mathematics and various other things. They attribute all the knowledge being passed down to them from the annunaki. So, being that to our current knowledge, no annunaki people(s) factually and undeniably are on the earth to meet the burden of proof of those stories claims - there is absolutely no evidence that anything written in the sumerian tablets pertaining to the origins of math and other things given from the annunaki to humans, is actually where it came from. Don't get me wrong, I do hope that one day we find enough evidence to confirm the sumerians claim, but as of now we just don't have it. And because of that, it may never catch on in the mainstream and you may likely be ridiculed by peers for even suggesting such a thing.
@@grant5392 Thanks for this interesting history. Why would I be ridiculed? I claim on multiple occasions that this is just a fictional story to talk about how math could have been invented.
@@ExistenceUniversity A separate reality hasn't been invented here. Fictional examples allow the exclusion of irrelevant details, and drive focus to the salient details, which appear in high relief. They're set in the very reality you inhabit every day.
ONE BUBBLE BOY COMING IN WITH ABSOLUTE SKITZOPOSTING! I am done with Mythomagical musings from larpers hiding in the halls of academia! Geometry is the FATHER! Mathematics is the CHILD! Mathematics is just, Dynamical Abstract Geometry That's it! Some of it has Geometric Representation but most of it doesn't.... it lives in the "imaginary" world of i's and rouge infinities avoided by renormalization.... its all poppyseeds! Sure Arithmetic and Algebra are fine.... but most of the rest is just gobbledygook science-fiction written with numbers. I am a Westerner living in AUS so I don't have anything to gain from this.... but we stole it all from the Indians.... the Vedics.... who used Astronomy as inspiration. Fibonacci was the only honest mathematician who gave credit.... people like Newt the Scrut put his name on RISHI KANADA'S LAWS OF MOTION and took credit for Calculus as well (Doesn't matter because Calculus is FALSE MATH!) John Napier solved problems of computation and uncovered the secrets of logarithms.... the rest just turned solutions into problems to get out of manual labor and to keep the scam going. Here... I wrote this for Mythomagicians! Mythomatics (Mathematics) There once was a mythomatical sage, Who worked on a geometrical page. With values exact, Pompous he'd act, But his proofs were more of a cage. In numbers, he found a grand tale, A myth in each numerical scale. Yet in his rush, To the abstract bus, He'd trip, slip, dip and leave reality pale.
You know you're onto something correct when so many kids attempt to emotionally tear your observations down.
Hahah. It's just one kid as far as I can tell.
Besides the ability to perceptually discriminate between units up to 7 or 8, @ExistenceUniversity asserted in his recent video that humans can also distinguish large ratios without counting. If you have 20 spears or 80 spears, you can clearly see that 20 is less than 80. As you said in your video, you would not be able to perceive 75 vs 80 vs 85 in the large pile, but we are doing something that makes comparing the groups immediately clear. I know some of our senses work on non-linear bases. Perhaps our visual system has two modes which we can use as the foundational fact to build our mathematical concepts.
The preliminary assumptions presented in the opening are not viable.
Which ones?
@Inductica the most obvious problem is trying to infer your working definition of "mathematics" that fits the concept of "invented", but more specifically stated is the idea that there could have been a human society "where no one even knows how to count yet" which is contrary to established biology. In sum, the published work of:
"Mathematical Cognition and Learning", by Michael J. Beran, Audrey E. Parrish, Theodore A. Evans, Volume 1, 2015, Pages 91-119, ISSN 2214-2568
says that according to research, primates are able to make ordinality judgments based on symbolic representations of numbers. This is a step above an beyond counting. It indicates that even the ancestors of the first humans could count innately. Counting for primates is similar to walking or eating. Its just something they can do.
As is borne out in the history of western mathematics, I would predict that some of man's earliest mathematics would come from music. But not because of harmony--because you very quickly need some kind of measurement system for precisely synchronizing events in time. Indeed, I posit that counting rhythms and cultural understandings of song and dance are probably man's earliest mathematics, even before we started forming sophisticated armies and trading with one another in sophisticated ways.
this depends largely on your definitions of both math and music. if counting is considered math - then primates naturally develop the skill much like walking or chewing. so you might need a working definition of music that can be applied to all adolescent primates.
Taxes. I think you don't get to have big armies before having taxes and before counting how much food you need for winter.
Interesting! But what about a mob army, not anything fancy and ordered?
Interesting video. Trying to put myself in the shoes of an ancient , fictional person like that helps me to think about all the ideas I hold and essentially take for granted.
Awesome!
8:09 ha! MArduk's soldeiers are wearing clothing with more than 7 tassels! Also they bands on their shoulders. We knew how to group and to count long before the neolithic. And the Egyptians were using scales LONG before the time of your "Marduk" in Babel.
@@idjles this is just meant as a fictional story.
Fun start! Thanks.
@@Cirnenric Much more to come!
Delighted to see you identify a method simpler than counting. This series is awesome. The rock carving adds to the story, but I think it has misled some of the commentators. This tribe from Babel is very ancient. They are not the people who had time to make such beautiful carvings or any monumental structures. What your story helps illustrate is the hierarchy of mathematical methods and to tease out methods we use all the time. We automated these comparison as well as the times tables. We don't normally notice them as a skill we learned or invented.
7:36 the 'shape of the moon' served Zhuge Liang and Zhou Yu just fine at the Battle of Chi Bi.
This was very fascinating to think about. I think a lot of people are missing the point of the video. I see the value in this.
Thanks!
you don't even need the one-to-one correspondance if you just put them into two pans on a balanced stick.
@@idjles what?
The quantities being compared are item quantities, not weights. And the uniformity of mass per item in this scenario has not been stipulated. So a comparison of weights here would not add value.
@@BuckPowers That's right, you are noticing how that his suggestion would break inductive order. I didn't even realize what his suggestion was at first.
@@Inductica you are completely overthinking it - scales work by symmetry - no numbers required.
Mathematics was invented before language. Language IS math. Counting was the beginning. Saying they invented language before counting is like saying they invented algebra before numbers.
Math might have been invented before language, true. What makes you say that language is math?
@@ExistenceUniversity This quote is a non-sequitir: though concept formation has a mathematical nature, that does not mean man needs explicit mathematical concepts before forming concepts. Rand also said somewhere else that the field of mathematics makes explicit what is implicit in the process of concept formation. So the mathematics inherent in forming concepts is implicit only, it is not the same as what I'm developing here, and what Walter was talking about, which is explicit mathematical concepts and methods.
@@ExistenceUniversity Exactly. Although in the case of Socrates = Man it would be a little more nuanced than that, as all men are not Socrates, so you'd likely use a uni-directional associative symbol rather than bidirectional association, but the general premise you're talking about is correct.
There's a recent interesting lecture you can find on RUclips called "Natural language as a cognitive computation on data-compressed grounded symbols" that covers this quite well and demonstrates the algebraic nature of language that is generally left out of the sentences we create for brevity, but still implied.
this is all over the place. Many animals have an innate ability to count - so it would be weird to say that counting was invented - was walking invented? Was burping invented? Is counting not "math"?
math is not interesting until you can communicate mathematically which may or may not require other skills that we could recognize as language first, but it seems like communication/language is required first before any recognizable as math. The reason for this is simple - for math to function as math - it requires an agreement against contradiction. First before we can do math, we have to agree that contradiction is forbidden. Only then can we "have math" other than innate counting.
So we need some natural language way to agree to exclude contradiction before we have anything like an effective math. It means natural language is a precursor to any significant math.
Importantly, for humans, as the present condition we find ourselves in - there is no better way to understand math other than that it is a language exactly in the same way English is a language and Spanish is a language. The difference is that math has a rule to exclude contradiction and that rule incites agreement on definitions before trying to express mathematical ideas. After that - its just another language.
@@oversquare6625 Animals don't count. There's a difference between counting and knowing whether one group is larger than another group intuitively. Counting is a very specific process, and it requires assigning labels and iterating on labels.
20 seconds in and my mind is already blown
Awesome!
The whole story seems to about the pragmatic significance of mathematics for survival which is mostly fine. Although as a platonist, i think it is a discovery not an invention. Also counting presupposes basic arithmetic capacity and i dont see a way around that being innate.
@@ReflectiveJourney In our next video, you will see how counting can be invented through observations and reasoning with knowledge established in this video.
Respectfully, I’ll give my opinion about the metaphysical nature of math, which is in strong opposition to Platonism: I think quantities and quantitative facts are out there in the world (such as the quantity of troops Marduk has) and that we *invent* mathematical *methods* to grasp those quantities. So the quantities are metaphysical, number, counting and other mathematical methods are inventions for grasping these facts and making inferences about their relationships between one another.
@@Inductica I would need to know more about what is meant by "quantities" and how is it different from numbers. Do you just mean that there are quantifiable facts like "there are 2 apples on the table" where "2" is the counting method used to state the fact.
Interesting view and i would agree with you that the methods and language to talk about mathematical structure is contingent on experience. This doesn't address the ontological issue though.
In my view, there are no perfect identities in the material world and it is a feature of our cognitive capacities that we track "close enough" patterns in the experience. Mathematics is the study of pure structures. I don't take a dualist view, the physical world is rationally constrained by the forms. The Pythagorean theorem is constraining the 3rd side of a triangle if you pick any two sides. It is not a generalization but a discovery about a geometrical structure (triangle). Even if we don't have a pure triangle in material world still any close enough structure to the triangle would be constrained by that. i am just probably rephrasing what Plato meant that experiential world is just an image of the forms but i believe he was pretty close.
The number "3" is a group with 3 units in it (at least, from the perspective of the quantity of units in the group).
@@UFO314159 Your definition references (and depends on) the term it's allegedly defining.
@@ReflectiveJourney Thank you for explaining your position clearly and respectfully. You have improved the quality of my comments section XD. Yes, that's very similar to Plato's view. In contrast, I think existence (the material world, as you put it) has full identity and that our senses give us data about that identity. If you'd like to know what my reason is for thinking that, check out the book "Objectivism, the Philosophy of Ayn Rand."
Why make a fiction? We have the ancient cuneiform tablets. We know that the origin story of writing is also the origin story of accounting. They invented credit money. The ancient near eastern maths were quite advanced. So, why the fiction?
Good question. Even if we adhered very closely to the ancient records, we would still have to fill in a lot of gaps regarding the actual observations and reasoning steps. Further, the actual history of math and physics involves lots of wrong turns and faulty reasoning. Our goal in this series is not to present a history of math, but rather to show its observational proof.
@@ExistenceUniversity You can see that these are situations which could happen, and that these are reasoning steps one could perform without knowing any math yet, the fictional nature of the narrative does not make it less rigorous.
While we know the sumerian tablets contain origin stories of mathematics and various other things. They attribute all the knowledge being passed down to them from the annunaki. So, being that to our current knowledge, no annunaki people(s) factually and undeniably are on the earth to meet the burden of proof of those stories claims - there is absolutely no evidence that anything written in the sumerian tablets pertaining to the origins of math and other things given from the annunaki to humans, is actually where it came from.
Don't get me wrong, I do hope that one day we find enough evidence to confirm the sumerians claim, but as of now we just don't have it. And because of that, it may never catch on in the mainstream and you may likely be ridiculed by peers for even suggesting such a thing.
@@grant5392 Thanks for this interesting history. Why would I be ridiculed? I claim on multiple occasions that this is just a fictional story to talk about how math could have been invented.
@@ExistenceUniversity A separate reality hasn't been invented here. Fictional examples allow the exclusion of irrelevant details, and drive focus to the salient details, which appear in high relief. They're set in the very reality you inhabit every day.
ONE BUBBLE BOY COMING IN WITH ABSOLUTE SKITZOPOSTING!
I am done with Mythomagical musings from larpers hiding in the halls of academia!
Geometry is the FATHER! Mathematics is the CHILD!
Mathematics is just, Dynamical Abstract Geometry
That's it!
Some of it has Geometric Representation but most of it doesn't.... it lives in the "imaginary" world of i's and rouge infinities avoided by renormalization.... its all poppyseeds!
Sure Arithmetic and Algebra are fine.... but most of the rest is just gobbledygook science-fiction written with numbers.
I am a Westerner living in AUS so I don't have anything to gain from this.... but we stole it all from the Indians.... the Vedics.... who used Astronomy as inspiration.
Fibonacci was the only honest mathematician who gave credit.... people like Newt the Scrut put his name on RISHI KANADA'S LAWS OF MOTION and took credit for Calculus as well (Doesn't matter because Calculus is FALSE MATH!)
John Napier solved problems of computation and uncovered the secrets of logarithms.... the rest just turned solutions into problems to get out of manual labor and to keep the scam going.
Here... I wrote this for Mythomagicians!
Mythomatics (Mathematics)
There once was a mythomatical sage,
Who worked on a geometrical page.
With values exact,
Pompous he'd act,
But his proofs were more of a cage.
In numbers, he found a grand tale,
A myth in each numerical scale.
Yet in his rush,
To the abstract bus,
He'd trip, slip, dip and leave reality pale.
Gene Ray's been-there-done-that over 25 years ago with his 4 corner simultaneous 4-day TIME CUBE.
"How Math _Could_ have been Invented"
"Wtf that's not how math was invented!"
🧍♂️
What's your reason for thinking it could not have been invented through these steps?